The main objective of this research is to assess the effectiveness of collective decisions for planning MRWs of the water pipelines in WDNs. For this purpose, a qualitative risk-based model was developed using a multi-criteria group DMM. Figure 1 illustrates the analytic steps of this model.
Figure 1 near here
As illustrated in Figure 1, the analytic steps of the developed model in this research are described separately below:
2.1. Step 1. Determining the decision criteria
To plan MRWs of the water pipelines in WDNs, identifying the effective variables in pipes prioritization is of great importance. Therefore, during the studies conducted in the previous years (Salehi et al. 2018a, Salehi et al. 2020), 42 and 48 criteria have been recognized as effective in determining the priority of pipe for rehabilitation. In the present study, the criteria affecting the priority of pipes for MRWs were developed to 50; and were divided into two categories of criteria and sub-criteria. Figure 2 shows the criteria and sub-criteria effective in the prioritization of pipe for MRWs.
Figure 2 near here
The model developed in this research is well-established, which can analyse any network with any number of criteria as well as any number of pipes. Furthermore, it is possible to assess network data with uncertainty using this model. Therefore, even networks with 1 or 2 criteria (accurate or imprecise) and with any number of pipes can be assessed by this model.
2.2. Step 2. Selecting the case studies
In this step, the case studies of research were selected. For this purpose, to consider a wide range of different regions of Iran, WDNs from the six provinces were chosen. Furthermore, for selecting these provinces, the various combinations of the numbers of decision makers/pipes/criteria were considered. Finally, a total of 76 decision-makers participated in these provinces. The dispersion of these six provinces and the numbers of decision makers/pipes/criteria in their water companies are shown in Figure 3.
Figure 3 near here
The number of pipes studied in this work was proposed by each water company. In addition, the numbers of criteria were determined based on data available in water companies. In this work, the selection of decision makers was based on their knowledge and work experience and was completely voluntary. The educational degrees and work experiences of these decision makers are presented in Table 1 in percentage.
Table 1
The profile of decision-maker experts in this research
No.
|
Water Company
of Province
|
Number of
Decision-Maker Experts
|
Education
|
|
Work Experience
|
Bachelor
|
Master
|
Ph.D
|
|
Year<10
|
10<Year<20
|
Year>20
|
1
|
Ardabil
|
9
|
44.44%
|
44.44%
|
11.11%
|
|
11.11%
|
44.44%
|
44.44%
|
2
|
Chaharmahal and Bakhtiari
|
14
|
64.28%
|
35.72%
|
0%
|
|
50%
|
42.86%
|
7.14%
|
3
|
Kurdistan
|
9
|
55.56%
|
44.44%
|
0%
|
|
44.44%
|
22.22%
|
33.34%
|
4
|
Razavi Khorasan
|
23
|
43.48%
|
47.83%
|
8.69%
|
|
34.78%
|
43.48%
|
21.74%
|
5
|
Sistan and Baluchestan
|
11
|
36.36%
|
63.64%
|
0%
|
|
27.27%
|
54.54%
|
18.19%
|
6
|
South Khorasan
|
10
|
40%
|
60%
|
0%
|
|
20%
|
40%
|
40%
|
2.3. Step 3. Determining the qualitative risk of pipes
In this study, to determine the pipe risk, the Pipe Failure Probability (PFP) and Pipe Failure Consequence (PFC) were assessed based on criteria determined in step 1. The method used for risk assessment in this research was based on analytic steps of the RC-WDSR model, which has been introduced in Salehi et al. (2020). For this purpose, in each case study, the conditions of the water pipelines were investigated in regards to 50 criteria. However, it should be noted that all criteria do not have the same role in pipe failure. Indeed, as shown in Table 2, some of these criteria are effective in PFP and others affect PFC. While, some of these criteria have a simultaneously influence on the probability and consequence of pipe failures (Table 2). The major information in Table 2 is obtained from Salehi et al. (2020).
Table 2
The criteria effective on probability or consequence of pipe failure (Salehi et al. 2020)
Criteria Effective on
Probability of Pipe Failure
|
Criteria Effective on
Consequence of Pipe Failure
|
Pipe Flow
|
Pipe Flow
|
Pipe Flow Velocity
|
Pipe Average Pressure
|
Pipe Average Pressure
|
Pipe Length
|
Pipe Age
|
Pipe Diameter
|
Pipe Length
|
Pipe Depth
|
Pipe Diameter
|
Pipe Maintenance Ease
|
Pipe Depth
|
Pipe Failure Rate
|
Pipe Roughness
|
Pipe Leakage Rate
|
Invulnerability of The Pipe in The Installation
|
Customers Complaints About The Water Quality
|
Pipe Lifetime
|
Residual Chlorine of Water in The Pipe
|
External Loading Capacity of Pipe
|
Water Age in the Pipe
|
External/Internal Corrosion of Pipe
|
Soil Type/Bedding around the Pipe
|
Non-Floatable Ability of Pipe
|
Excavation Ease of the Soil around the Pipe
|
Heat Resistance of Pipe
|
Pathway Type in top of the Pipe
|
Earthquake Resistance of Pipe
|
Pathway Cover in top of the Pipe
|
Pipe Failure Rate
|
Pathway Cover Thickness in top of the Pipe
|
Pipe Leakage Rate
|
Pipe Location in the Pathway
|
Residual Chlorine of Water in The Pipe
|
Pathway Level in top of the Pipe
|
Water Age in the Pipe
|
Customers Type of Pipe
|
Soil Type/Bedding around the Pipe
|
Combination of Customers of Pipe
|
Soil Corrosion around the Pipe
|
Number of Customers of Pipe
|
Pathway Type in top of the Pipe
|
Customers Density of Pipe
|
Pathway Cover in top of the Pipe
|
Pipe Customers’ Building Age
|
Pathway Cover Thickness in top of the Pipe
|
Number of Connections in the Pipe
|
Pathway Traffic Load in top of the Pipe
|
Number of Junctions in the Pipe
|
Pipe Location in the Pathway
|
Number of Control Valves in the Pipe
|
Number of Connections in the Pipe
|
Number of Pressure Valves in the Pipe
|
Number of Junctions in the Pipe
|
Number of Hydrants in the Pipe
|
Number of Control Valves in the Pipe
|
Implementation/Installation Cost of Pipe
|
Number of Pressure Valves in the Pipe
|
Operational Cost of Pipe
|
Number of Hydrants in the Pipe
|
Renewal Cost of Pipe
|
Installation Quality of Pipe
|
Return on Investment of the Pipe Renewal
|
|
Municipal/Social Importance of Pipe
|
|
Political/Security Importance of Pipe
|
|
Pipe Water Supply Importance to Customers
|
|
Pipe Importance in Respect To Other Urban Facilities
|
|
Pipe Importance in Urban Management Plans
|
Since there is deep uncertainty in the WDNs data and some numerical information of these networks are imprecise (Wang et al. 2019, Khameneh et al. 2019, Marques and Cunha 2020, Fletcher et al. 2017, Torres et al. 2009, Sadiq et al. 2008, Kapelan et al. 2004), quantitative risk analysis of pipe failure has been not considered in this study. Thus, the linguistic-fuzzy (qualitative) risk-based method was used to determine the condition of the pipes in relation to each criterion. Additionally, this method could be useful for collective decisions due to the hesitation in group decision-making (Wu et al. 2020, Tang et al. 2019, Madani et al. 2014, Vahdani et al. 2011, Jiang et al. 2011, Anisseh and Mohd Yusuff 2011). In this regard, to determine the pipe condition the form of Table 3 was generated.
Table 3
The form used in this research to determine the pipe qualitative risk
Pipe Number ……
|
Pipe Location (Address):
|
|
|
No.
|
Sub-Criteria
|
Determination of the Qualitative Risk in respect to each Sub-Criterion
Using Linguistic/Fuzzy Values in relating to Pipe Condition
|
Very Low Risk
|
Low
Risk
|
Relatively
Low Risk
|
Medium Risk
|
Relatively High Risk
|
High
Risk
|
Very High Risk
|
(0,0,1,2)
|
(1,2,2,3)
|
(2,3,4,5)
|
(4,5,5,6)
|
(5,6,7,8)
|
(7,8,8,9)
|
(8,9,10,10)
|
01
|
Pipe Flow
|
Very Low Flow
|
Low Flow
|
Relatively Low Flow
|
Medium Flow
|
Relatively High Flow
|
High Flow
|
Very High Flow
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
50
|
Pipe Importance in Urban Management Plans
|
Very Low Importance of Pipe
|
Low Importance of Pipe
|
Relatively Low Importance of Pipe
|
Medium Importance of Pipe
|
Relatively High Importance of Pipe
|
High Importance of Pipe
|
Very High Importance of Pipe
|
Table 3 near here
In this table, each criterion was divided into seven categories. This categorization was not based on numerical classification, but on linguistic-fuzzy division. The condition of each pipe in relation to each criterion was determined based on the available field data as well as the knowledge and experience of the network operator who filled the form (Table 3). The fuzzy numbers assigned to linguistic values were trapezoidal fuzzy numbers. A trapezoidal fuzzy value (\(\tilde{\text{x}}=({\text{x}}_{\text{m}\text{i}\text{n}},{\text{x}}_{\text{a}\text{v}\text{e}1},{\text{x}}_{\text{a}\text{v}\text{e}2}, {\text{x}}_{\text{m}\text{a}\text{x}})\)) is introduced as a four-component number, in which \({\text{x}}_{\text{m}\text{i}\text{n}}\)and \({\text{x}}_{\text{m}\text{a}\text{x}}\) indicate the minimum and maximum possible values, whereas, \({\text{x}}_{\text{a}\text{v}\text{e}1}\)and \({\text{x}}_{\text{a}\text{v}\text{e}2}\) show the most probable values for a given number. The characteristic function of this number follows in below (Anisseh and Mohd Yusuff 2011, Salehi et al. 2018b):
\({\mu }_{\tilde{A}}\left(\text{x}\right)=\left\{\begin{array}{c}0 x\le {\text{x}}_{\text{m}\text{i}\text{n}}\\ \\ \frac{\text{x} – {\text{x}}_{\text{m}\text{i}\text{n}}}{{\text{x}}_{\text{a}\text{v}\text{e}1}- {\text{x}}_{\text{m}\text{i}\text{n}}} {\text{x}}_{\text{m}\text{i}\text{n}}\le x\le {\text{x}}_{\text{a}\text{v}\text{e}1}\\ \\ \\ 1 {\text{x}}_{\text{a}\text{v}\text{e}1}\le x\le {\text{x}}_{\text{a}\text{v}\text{e}2}\\ \\ \frac{{\text{x}}_{\text{m}\text{a}\text{x}} – \text{x}}{{\text{x}}_{\text{m}\text{a}\text{x}}- {\text{x}}_{\text{a}\text{v}\text{e}2}} {\text{x}}_{\text{a}\text{v}\text{e}2}\le x\le {\text{x}}_{\text{m}\text{a}\text{x}}\\ \\ \\ 0 x\ge {\text{x}}_{\text{m}\text{a}\text{x}}\end{array}\right.\) (1)
2.4. Step 4. Planning the maintenance-rehabilitation works of pipes
In this study, filling the form of the pipes' qualitative risk (Table 3) by the network operator, the priority and renovation strategy of pipes were determined. To analyse this form, a multi-criteria decision model was developed based on the TOPSIS method, which has been introduced firstly by Yoon and Hwang (1981). The reason for using this method is its significant ability in planning the design and rehabilitation of water and sewer networks (Salehi et al. 2018a, Tscheikner-Gratl et al. 2017, Wu and Abdul-Nour 2020); Whereas, the other methods (e.g. AHP) do not have the desired capability to analyse decision-making problems where the number of criteria and alternatives increase (Tscheikner-Gratl et al. 2017, Wu and Abdul-Nour 2020, RazaviToosi and Samani 2019, Islam et al. 2013, Yazdani et al. 2012). In addition, considering the fuzzy-linguistic values used in this research, the model developed in this research was based on Fuzzy TOPSIS.
Since the criteria considered in this research had different scales, in the first stage of the Fuzzy TOPSIS model, the fuzzy values related to the pipes' qualitative risk were changed to descaled fuzzy values based on the formula presented below:
\({\tilde{\text{r}}}_{\text{m}\text{c}}^{ }= \left(\frac{{\text{x}}_{\text{min}\left(\text{m}\text{c}\right)}^{ }}{{\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}}, \frac{{\text{x}}_{\text{ave}1\left(\text{m}\text{c}\right)}^{ }}{{\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}},\frac{{\text{x}}_{\text{ave}2\left(\text{m}\text{c}\right)}^{ }}{{\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}},\frac{{\text{x}}_{\text{max}\left(\text{m}\text{c}\right)}^{ }}{{\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}}\right)\)
\({\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}= {}_{\text{m} }{}^{\text{M}\text{a}\text{x}}{ \text{x}}_{\text{max}\left(\text{m}\text{c}\right)}^{ }\) (2)
\({\tilde{\text{r}}}_{\text{m}\text{c}}^{ }\): Descaled fuzzy value of the mth water pipeline in related to cth criteria
m = 1,2,…,m, c = 01,02,…,50
Afterwards, two target and theoretical pipes which have the highest and least failure risk were calculated using the following formula:
Pipe with highest risk (the most critical pipe for maintenance-rehabilitation works) =\({\text{V}}^{+}\)
\({\text{V}}^{+}= \left\{{\tilde{\text{v}}}_{01}^{+},\dots \dots \dots ,{\tilde{\text{v}}}_{\text{c}}^{+}\right\}\), \({\tilde{\text{v}}}_{\text{c}}^{+}=\underset{\text{m}}{\text{Max}} \left\{{\tilde{\text{r}}}_{\text{m}\text{c}}^{ }\right\}\) (3)
Pipe with least risk (the least important pipe for maintenance-rehabilitation works) =\({\text{V}}^{-}\)
\({\text{V}}^{-}= \left\{{\tilde{\text{v}}}_{01}^{-},\dots \dots \dots ,{\tilde{\text{v}}}_{\text{c}}^{-}\right\}\), \({\tilde{\text{v}}}_{\text{c}}^{-}=\underset{\text{m}}{\text{Min}} \left\{{\tilde{\text{r}}}_{\text{m}\text{c}}^{ }\right\}\) (4)
These best and worse pipes are calculated only to measure the distances of real water pipelines from them for determining the pipes' priorities/strategies for MRWs. Indeed, these pipes are theoretical and do not exist in real WDNs.
In the next stage, the distance of each water pipeline was measured from the pipes with the highest and least risks. This distance was determined using the below formula:
Distance of water pipeline from the pipes with the highest/least risk\(={\text{S}}_{\text{m}}^{ \pm }\)\({\text{S}}_{\text{m}}^{\text{ }\pm } = \sum _{\text{c}=01}^{\text{c}}\text{d}\left({\tilde{\text{v}}}_{\text{mc}}^{ },{\tilde{\text{v}}}_{\text{c}}^{\pm }\right)\)
\(=\sqrt{\frac{1}{4}\left[{ \left({\text{v}}_{\text{min}\left(\text{m}\text{c}\right)}^{ }{- \text{v}}_{\text{min}\left(\text{c}\right)}^{\pm }\right)}^{2}+{\left({\text{v}}_{\text{ave}1\left(\text{m}\text{c}\right)}^{ }{- \text{v}}_{\text{ave}1\left(\text{c}\right)}^{\pm }\right)}^{2}+{\left({\text{v}}_{\text{ave}2\left(\text{m}\text{c}\right)}^{ }{- \text{v}}_{\text{ave}2\left(\text{c}\right)}^{\pm }\right)}^{2}+{\left({\text{v}}_{\text{max}\left(\text{m}\text{c}\right)}^{ }{- \text{v}}_{\text{max}\left(\text{c}\right)}^{\pm }\right)}^{2}\right]}\) (5)
Finally, the priority of each water pipeline for MRWs was determined by the following formula:
\(\text{P}\text{i}\text{p}\text{e} \text{p}\text{r}\text{i}\text{o}\text{r}\text{i}\text{t}\text{y} \text{i}\text{n}\text{d}\text{e}\text{x} \text{f}\text{o}\text{r} \text{M}\text{R}\text{W}\text{s} =\frac{{{\text{S}}_{\text{m}}^{\text{ }-}}_{\left({by all studied criteria}\right)}}{{{\text{S}}_{\text{m}}^{\text{ }+}}_{\left({by all studied criteria}\right)}+{{\text{S}}_{\text{m}}^{ -}}_{\left({by all studied criteria}\right)} }\) (6)
This index is a number between zero and one, which the closer it is to the number 1, the higher the priority of the water pipeline for MRWs.
In addition, to determine the strategy of MRWs for each water pipeline two other indices were determined using the same formula of number 6 as follows:
\(\text{P}\text{F}\text{P} \text{i}\text{n}\text{d}\text{e}\text{x} =\frac{{{\text{S}}_{\text{m}}^{\text{ }-}}_{\left({by criteria effective in Pipe Failure Probability }\right({PFP}\left)\right)}}{{{\text{S}}_{\text{m}}^{\text{ }+}}_{\left({by criteria effective in PFP}\right)}+{{\text{S}}_{\text{m}}^{\text{ }-}}_{\left({by criteria effective in PFP}\right)} }\) (7)
\(\text{P}\text{F}\text{C} \text{i}\text{n}\text{d}\text{e}\text{x} =\frac{{{\text{S}}_{\text{m}}^{\text{ }-}}_{\left({by criteria effective in Pipe Failure Consequence }\right({PFC}\left)\right)}}{{{\text{S}}_{\text{m}}^{\text{ }+}}_{\left({by criteria effective in PFC }\right)}+{{\text{S}}_{\text{m}}^{\text{ }-}}_{\left({by criteria effective in PFC}\right)} }\) (8)
Similar to the pipe priority index, these indices are numbers between zero and one. Considering the measured PFP and PFC indices of each water pipeline, the MRWs strategy of pipes were determined using the graph illustrated in Figure 4. This figure was obtained from the research of Salehi et al. (2020).
Figure 4near here
As previously mentioned in Figure 1, this research has been conducted in two methods. In the first method, the decision criteria were weighted using group decision making. For this purpose, the nominal group technique as one of the main methods of group DMMs (Figueira et al. 2005) was used. Hence, to assess the viewpoints of the decision makers, a decision form was provided and presented to experts using the instant message (Kilgour and Eden 2010). The general format of this form was obtained from the previous studies (Salehi et al. 2018a, Salehi et al. 2020). Table 2 shows the form used in this study for weighting the criteria. It should be mentioned that since the main objective in this research is assessing the effect of collective decision for planning the MRWs of the water pipelines, the weighting of experts is omitted for a correct judgment of the effect of expert viewpoints.
Table 4
The group decision-making form used in this research
Expert Profile
|
First Name
|
Last Name
|
Organization
|
Position
|
Education
|
Year of Work Experience
|
Question:
How much the criteria presented in below are effective
in planning maintenance-rehabilitation works of water pipeline in water distribution networks?
|
Code
|
Sub-Criteria
|
Very low
|
Low
|
Relatively low
|
Medium
|
Relatively high
|
High
|
Very high
|
(0,0,0.1,0.2)
|
(0.1,0.2,0.2,0.3)
|
(0.2,0.3,0.4,0.5)
|
(0.4,0.5,0.5,0.6)
|
(0.5,0.6,0.7,0.8)
|
(0.7,0.8,0.8,0.9)
|
(0.8,0.9,1,1)
|
01
|
Pipe Flow
|
GD101
|
GD201
|
GD301
|
GD401
|
GD501
|
GD601
|
GD701
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
.
.
.
|
50
|
Pipe Importance in Urban Management Plans
|
GD150
|
GD250
|
GD350
|
GD450
|
GD550
|
GD650
|
GD750
|
GDic : The ith linguistic value assigned to cth criterion by expert to determine the importance of cth criterion
i= 1(very low),2 (low),…,7 (very high), c = 01,02,…,50
|
As shown in Table 4, each of the linguistic values is related to a trapezoidal fuzzy number. Accordingly, the weight obtained for each criterion would be a fuzzy value. This value was achieved using the following formula:
\({\tilde{\text{w}}}_{\text{c}}\) \(= \left({w}_{\text{min}\left(\text{c}\right)}, {w}_{\text{a}\text{v}\text{e}1\left(\text{c}\right)},{w}_{\text{a}\text{v}\text{e}2\left(\text{c}\right)},{w}_{\text{m}\text{a}\text{x}\left(c\right)}\right)\)
\({\tilde{\text{w}}}_{\text{c}}\) \(=\) \(\left({}_{\text{k}}{}^{\text{m}\text{i}\text{n}}\left\{{w}_{\text{min}\left(\text{c}\right)}\right\}, \frac{\sum _{1}^{\text{k}}{\text{w}}_{\text{a}\text{v}\text{e}1\left(\text{c}\right)}}{\text{k}},\frac{\sum _{1}^{\text{k}}{\text{w}}_{\text{a}\text{v}\text{e}2\left(\text{c}\right)}}{\text{k}},{}_{\text{k}}{}^{\text{m}\text{a}\text{x}}\left\{{w}_{\text{max}\left(\text{c}\right)}\right\}\right)\)
(9)
\({\tilde{\text{w}}}_{\text{c}}\): weight of cth criteria in the format of the fuzzy value; c = 01,02,…,50
k = the numbers of decision-maker experts
Furthermore, after descaling the fuzzy values (first stage of Fuzzy TOPSIS model), the descaled fuzzy values were weighted using the formula as follows:
\({ \tilde{\text{v}}}_{\text{m}\text{c}}^{ }= \left(\frac{{\text{x}}_{\text{min}\left(\text{m}\text{c}\right)}^{ }}{{\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}}.{w}_{\text{min}\left(\text{c}\right)}, \frac{{\text{x}}_{\text{ave}1\left(\text{m}\text{c}\right)}^{ }}{{\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}}.{w}_{\text{a}\text{v}\text{e}1\left(\text{c}\right)},\frac{{\text{x}}_{\text{ave}2\left(\text{m}\text{c}\right)}^{ }}{{\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}}.{w}_{\text{a}\text{v}\text{e}2\left(\text{c}\right)},\frac{{\text{x}}_{\text{max}\left(\text{m}\text{c}\right)}^{ }}{{\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}}.{w}_{\text{m}\text{a}\text{x}\left(c\right)}\right)\) \({\text{x}}_{{\text{m}\text{a}\text{x}}^{{+}_{\left(\text{c}\right)}}}={}_{\text{m} }{}^{\text{M}\text{a}\text{x}}{ \text{x}}_{\text{max}\left(\text{m}\text{c}\right)}^{ }\) (10)
\({\tilde{\text{v}}}_{\text{m}\text{c} }^{ }\): Weighted descaled fuzzy value of the mth pipe in related to cth criteria
m = 1,2,…,m, c = 01,02,…,50
In the second method of this research, analytic steps of Fuzzy TOPSIS were performed without using group decision making. Finally, the results of two methods including group DMM and no-group DMM were compared.